help-39

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[naive parcel]

hello please ping me if someone can help me with this

<@&286206848099549185>

[warm current]

!15m

[pearl pond]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[naive parcel]

sorry

[pearl pond]

@naive parcel Has your question been resolved?

[naive parcel]

<@&286206848099549185>

[pearl pond]

@naive parcel Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[midnight reef]

how do one approach these problems?

[safe drum]

For the first part

5^(2n) Mod 7 = 2^(2n) Mod 7

3.2^(5n-2) = (-4)(2^(5n-2)) = -(2)^(5n)

Now you add them

2^2n -2^5n mod 7 = (-28)2^n mod 7 = 0

[pearl pond]

@midnight reef Has your question been resolved?

[midnight reef]

I don't understand this part

[pearl pond]

@midnight reef Has your question been resolved?

[ripe shoal]

what exactly does summation mean in this q

[pearl pond]

@midnight reef Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[regal sequoia]

"Let D be the flat area bounded by the parabola y = x^2 and the line y = 1. Calculate"

[wet osprey]

What have you tried?

[regal sequoia]

nothing i honastly have no clue what to do

[wet osprey]

Have you seen integrals like this before?

[regal sequoia]

i have delt with single ones but never dubble ones

[wet osprey]

This should not be the first double integral you do

There should be easier ones to start with

[regal sequoia]

i kind of have to start with this

[final fiber]

have you been taught double integrals before

[regal sequoia]

yes in classes

[wet osprey]

Something like let $D = {(x, y)| 0\leq x \leq 1,, 0\leq y\leq 1}$, find
$$\iint_D 1 dA$$

[jolly parrot]

Frosst

[regal sequoia]

but we just started them and we had like one class on them

[jolly parrot]

Frosst

[final fiber]

if you really wanna do this then graph the area to integrate over and try to establish bounds for x and y

but if it's your first one then yea, maybe try something simpler first

[wet osprey]

This is as simple as it gets

[regal sequoia]

this is just the double intergal and the D under it from the first questions is the area in witch we are integrating

@rough forge

[final fiber]

just realized you can't easily integrate this, but you have to notice something in the integrand

[pearl pond]

@regal sequoia Has your question been resolved?

Channel closed

Closed by @regal sequoia

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[old marsh]

topic: hitting times of a brownian motion where T_a represents the first time the BM hits a

[old marsh]

can someone explain how we went from that first blue part to the expression under the arrow?

anyone understand this so called ‘reflection principle’ ?

[pearl pond]

@old marsh Has your question been resolved?

[old marsh]

i dont get this

[pearl pond]

@old marsh Has your question been resolved?

[fleet delta]

discord.gg/math

[pearl pond]

@old marsh Has your question been resolved?

[cursive wolf]

I'm not proficient at this stuff but could it be that we're shifting all times by 1?

$P(T_{-1} < T_3 | T_1 < T_{-1}) = P(T_{-2} < T_2 |T_0 < T_{-2})$?

[jolly parrot]

Lartomato

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cursive wolf]

I wonder if that's meaningful. Because T_0 < T_{-1} is obviously always true, the r.h.s reduces to P(T_{-2} < T_2). Just need to argue why this shift is reasonable,

[cursive wolf]

.close

[pearl pond]

Channel closed

Closed by @cursive wolf

Use .reopen if this was a mistake.

[old marsh]

.reopen

[pearl pond]

✅

[old marsh]

hmmm

[cursive wolf]

it might really not be reasonable hahaha

i've never done a course on this unfortunately

[old marsh]

ah i c

lemme give it some thought

honestly i think the 'shift by 1' makes sense

because the graph has to cover the same amount of change in function

so like P(T2 < T-2) is equal in distribution (or something) to P(T4 < T0) for example

oh maybe by independent and stationary increments?

i think that may be it actually lol

thanks @cursive wolf !

[cursive wolf]

yeah i'm just wondering still

idk it feels like there's some subtleties but i'm not getting it lmao

it sounds like it gave you some ideas so good luck!

the conditional part confuses me

[old marsh]

yes i think a vertical shift makes a lot of sense

[old marsh]

yea i'll figure it out

something like this, just translated up a unit

yes independent and stationary increments works with that quite nicely i think

alright

.close

[pearl pond]

Channel closed

Closed by @old marsh

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[charred ocean]

No, because that’s just -infty because infinity is not a number

Maybe $x*(-1)^x$ would work

[jolly parrot]

Pixelius

[vale sentinel]

What about tan(sqrtx)

What do you mean

Ohh

Right mb

xsinx

What about that

Oops

I mean

xsin(sqrtx)

It looks ok to me

[pearl pond]

Channel closed

Closed by @reef cipher

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dense plover]

can someone help me with question 24 please

[tall flint]

!status

[pearl pond]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[dense plover]

i know im trying to find the mean

wait no

the sample

but i dont have the mean

so how am i supposed to use the formula

this one

i need the mean

to find the sample

[tall flint]

no you don't

you're asked to find the sample size such that the confidence interval is of the form (estimate) +/- 15

you can construct this without the mean

[pearl pond]

@dense plover Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drowsy bramble]

I haven't the tiniest grasp on actually doing integration by by parts

[drowsy bramble]

anyone able to explain?

[sharp vigil]

given two functions $u(x)$ and $v(x)$ we have the formula [ \int u v' dx = uv - \int u' v dx ]

[jolly parrot]

pnoןɔ

[tepid ether]

Sir i would recommend watching the following video:

https://www.youtube.com/watch?v=2I-_SV8cwsw

This is how i learned IBP

[drowsy bramble]

the tabular method

[tepid ether]

The tabular method is amazing

[drowsy bramble]

going to lose it

[tepid ether]

Why sir?

Do not do that.

[fossil jewel]

do it

[neon sand]

BPRP!!!

[tepid ether]

Sir this is no allowed by the #rules . any last words?

[indigo pewter]

?

what

[woeful stump]

what rule?

[drowsy bramble]

are any of you avalible to call?

[tepid ether]

No.

[drowsy bramble]

np

[tepid ether]

Do you still have doubts even after the BPRP video?

[drowsy bramble]

yes

[sharp vigil]

1. choose a v' that has an easy integral
2. choose u that has an easy derivative
   ( you can choose to remember LIATE for which ones to try first)
3. compute u' and v
4. evaluate the new integral

[pearl pond]

@drowsy bramble Has your question been resolved?

Channel closed

Closed by @drowsy bramble

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crisp brook]

Hii what would the graph be

[crisp brook]

Isnt the period 2?

Cos 2pi/pi

[hushed fable]

Yeah should be

[crisp brook]

But the bottom right answer didnt work

[hushed fable]

I feel like it should

Idk what the problem is

[woeful stump]

yeah it should be #4

[crisp brook]

Ohh wait i just tried again and it worked :DD

Ty!

.close

[pearl pond]

Channel closed

Closed by @crisp brook

Use .reopen if this was a mistake.

[hushed fable]

lol ok

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[zinc parrot]

can someone help with this problem

[wet osprey]

Where are you stuck?

[zinc parrot]

like evehrbring i’m not sure what it means

i recently startrrd matrix stuff

we review

don’t remmeber it much

[wet osprey]

Do you know what elements row operations are?

[zinc parrot]

no 😭

[wet osprey]

Have a look through your notes

[pearl pond]

@zinc parrot Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[plucky wing]

is the value of a = 1 since it starts off as 100% effective

[vale sentinel]

Yh

[cosmic garnet]

yes

[pearl pond]

@plucky wing Has your question been resolved?

Channel closed

Closed by @plucky wing

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[verbal lotus]

i have a question

[vale sentinel]

Ask

[glacial scroll]

i dont have a quewestion

[cosmic garnet]

then dont ask

[arctic siren]

We can't answer it if you never post it

[verbal lotus]

what does it mean when a function question has x is not = -2

does it affect my solving

[glacial scroll]

what is the context of the question

can u send the original problem

[zealous dagger]

x can’t equal -2 :)

[vale sentinel]

[arctic siren]

Post the whole question, please

[vale sentinel]

Restriction?

Probably asymptote

[arctic siren]

Well here it's mainly just to be formal

Try plugging in g(-2)

you'll see why it has to be excluded

[verbal lotus]

oh alr

[arctic siren]

yeah you get 1/0, which is undefined

so technically, this function is only defined on every number that is not -2

but in practice, you usually ignore this.

[verbal lotus]

bless

.close

[pearl pond]

Channel closed

Closed by @verbal lotus

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[regal sequoia]

"Let D be the flat area bounded by the parabola y = x^2 and the line y = 1. Calculate..."

[final fiber]

this was from yesterday right

have you looked into double integrals

[pearl pond]

@regal sequoia Has your question been resolved?

[regal sequoia]

yes but i still dont know how to solve this

[final fiber]

have you tried putting the bounds in?

are you having trouble with the bounds or the sin term

[regal sequoia]

Both honestly I don’t know what do start with

[final fiber]

graph the area to integrate over

[regal sequoia]

Do we not get x = +-1?

[final fiber]

no, they meant the area bounded by the curves y = x^2

and y = 1

[regal sequoia]

Yes for y but do we not need the bounds for x as well?

[final fiber]

region D is this right?

[regal sequoia]

Yes

[final fiber]

so bounds for y would be x^2 to 1, you agree?

[regal sequoia]

Yes

[final fiber]

and bounds for x would be -1 to 1

[regal sequoia]

Yes

[final fiber]

so its integrating from x^2 to 1 with respect to y, and then -1 to 1 with respect to x

now, you can start integrating

[regal sequoia]

Do we get -cos(2xy^2) / 2y + x^2y^2 / 2

For the first integral

[final fiber]

no

integral of sin(2xy^2) dy isn't -cos(2xy^2)/2y

in fact, i don't think you can integrate sin of constant times y^2

instead, you have to notice something about the region you're integrating over

(it's symmetric along the y-axis)

[regal sequoia]

Okay

[final fiber]

(integrate sin(2xy^2) separately and try substituting u = -x)

[regal sequoia]

1/4x (cos(x) + C)

[regal sequoia]

Why does it become -I?

[final fiber]

because sin(-uy^2) = -sin(uy^2)

[pearl pond]

@regal sequoia Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slow void]

<@&286206848099549185> i need clearance

[pearl pond]

@slow void Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sleek junco]

why no +C in this

[sleek junco]

is it cuz they specify 0<t<9 limits so +C is ignored?

oh nvm

im blind

.close

[pearl pond]

Channel closed

Closed by @sleek junco

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rapid bough]

I think it’s 7 since it looks like a 7x7 jordan block

[tropic saddle]

does it?

[rapid bough]

the zeroes are throwing me off

[tropic saddle]

imagine all of the diagonal was 17

what then

[rapid bough]

to be honest i’m not sure

[tropic saddle]

well you said jordan block

what is a jordan block

[rapid bough]

Oh wait there’s no numbers on the diagonal and the jordan blocks are like the eigenvalues with the same multiplicity and ones above them along the higher diagonal

If there were all 17s would there be 3?

[tropic saddle]

3 what

[rapid bough]

jordan blocks

[tropic saddle]

yes

and now is there a difference whether there is 17 on the diagonal or 0?

[rapid bough]

I don’t think there is one

[tropic saddle]

so can you answer the question then?

[rapid bough]

is the degree of the minimal polynomial related to jordan blocks in the same way that it’s degree is related to num of eigen values?

I guess i’m asking does 0 have multiplicity 7 here or is there some other relation due to different jordan blocks

[tropic saddle]

well, which multiplicity

there are two kinds

[rapid bough]

I’m not sure and i’m not sure how exactly to relate either to dim min poly

[tropic saddle]

I suggest to actually compute it for this matrix

that might make it clearer

first compute the char poly

[rapid bough]

(X-0)^7 no?

[tropic saddle]

yes

so what do you know about the min poly?

[rapid bough]

it’s the smallest polynomial such that p(A) = 0 and it divides the char polynomial

[tropic saddle]

ok, what are the divisors of X^7?

[rapid bough]

X

and X^7

[tropic saddle]

no you are missing several

for example if X is a divisor, then also X^7/X is a divisor

[rapid bough]

Oh yea

[tropic saddle]

and what about X^2

[rapid bough]

X^i
0 leq i leq 7

[tropic saddle]

ok

so now the question is, what is the smallest i with A^i=0

compute A,A^2,...

[rapid bough]

wait i’m just realizing it’s an 8x8 matrix

A^4=0

[tropic saddle]

ok then what is the min poly

and how was this calculation related to the jordan blocks

[pearl pond]

@rapid bough Has your question been resolved?

[rapid bough]

thank you

[pearl pond]

Channel closed

Closed by @rapid bough

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[formal marten]

How to integrate this

[light helm]

chian rule or u-sub

consider doung the substitution
u = 1-x^2

[formal marten]

How would chain rule work

[light helm]

the same way

just without explicitly subbing

sub just makes the calculation process easier

[formal marten]

No as in what do we do could you show the working out

[abstract kraken]

Yo

[light helm]

do the work with sub first

[abstract kraken]

Anyone free?

[light helm]

#❓how-to-get-help

[pearl pond]

@formal marten Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brittle granite]

how would i do this using trig

[unborn abyss]

,rccw

[weak lintel]

let BP=x

PA=3-x

so you know sin α and sin β

also cos α and cos β

sin θ = sin (α+β)

just maximize sin θ

[brittle granite]

wait whats sin(a+b) as a value

[weak lintel]

sin(a+b)=sina cosb + cosa sinb

[brittle granite]

do i need to find derivative of that

and make it equal 0

[weak lintel]

yes

maybe there is easier solutions

that needs a lot of caculation

calculate tan a+b is easier

tan a = x/2 tan b = (3-x)/5

tan (a+b) = (tan a + tan b)/(1-tan a*tan b)

[brittle granite]

i find derivative of this?

[weak lintel]

yes

the result should be this

so x = 2*sqrt(5)-2

[pearl pond]

@brittle granite Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[formal marten]

Should I use integration by parts for this? <@&286206848099549185>

[fluid axle]

Try it

You prolly won't get very far

[formal marten]

Yeah

Doesn’t work

What’s best to do

[fluid axle]

It's just a u sub here essentially

[formal marten]

How tho

[compact veldt]

U can see the answer pretty easily ngl

[hushed vale]

u = x^2

[formal marten]

Would this be correct

[limber ravine]

This is not helpful for someone trying to learn.

[sharp smelt]

eh, try a u-sub

[formal marten]

How do we know what to take u as usually in these questions

[hushed vale]

intuition

its pretty clear that differenciation of x^2 will let you cancel x

just gotta keep practicing

[limber ravine]

If you can see it on the form f'(x) · g(f(x)) for some functions f and g, then u = f(x) is usually the way to go

[formal marten]

yeah makes sense thank you so much, also it usually doesn’t matter if we multiply c by the number in front as it’s a constant anyway yes?

[limber ravine]

In your example you can rewrite\

$\int x \cdot e^{x^{2}} ; \dd x = \frac{1}{2} \cdot \int 2x \cdot e^{x^{2}} ; \dd x$\

And then you can apply this

[jolly parrot]

Mikkel Angelo

[formal marten]

Alright thanks a lot

[limber ravine]

[formal marten]

.close

[pearl pond]

Channel closed

Closed by @formal marten

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[elder glen]

Hey guys

[elder glen]

I’m new

Have few questions

[jagged burrow]

[elder glen]

Yup

So umm what is substitution method in algebra

[jagged burrow]

can u ask a more specific question

[pearl pond]

@elder glen Has your question been resolved?

[elder glen]

Yes

What is the substitution method

In algebra

[spark belfry]

Replacing a variable for example $ (x+2)^2 = 9 $

You can sub u = x+2

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[amber onyx]

So i'm trying to solve a special relativity problem in maple, but i get RootOf(...) instead of the wanted solution. Does anyone know how i can make it find the right solution? (this was the best place i could think of to ask the question. Let me know if you know a better place)
Image

[pearl pond]

@amber onyx Has your question been resolved?

[pearl pond]

@amber onyx Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[chilly flame]

There are these two similar problem. For some reason, one of them ended up with the sin addition onto the formula, and the other one has e. I’m not sure why.

[thin sigil]

These are second order ode's right?

[chilly flame]

I think so

[thin sigil]

as far as I remember their solutions usually end up being some linear combination of sines, cosines and e's, but just because the problem statement might seems similiar the solution can be vastly different in many cases

[chilly flame]

That’s what I’m realizing, I just don’t see where they are pulling which form it should take from

They just dump the T(t) formula

[thin sigil]

Yeah, math books like to skip details

Here's some references

https://tutorial.math.lamar.edu/classes/de/introsecondorder.aspx

https://tutorial.math.lamar.edu/classes/de/VariationofParameters.aspx

[chilly flame]

Good old Paul

[thin sigil]

I don't remember the specifics of these (did em a long time ago) but I think you assume the answer to be some combination and work your way from there

[chilly flame]

These equations don’t look like those

Guess I’ll just keep poking around

Those pages basically just say to take a guess

[thin sigil]

I don't remember completely but I think you're supposed to recognize some pattern from the problem formulation to know which format the solution will be (what linear combination of sin, cos, e or ln) and work your way back

so it is a guessing game, kinda

[chilly flame]

On a much easier note, how would I tell if an equation is odd or even for the fourier series?

Do I just plug-in a number and see what it does?

I know odd means like diagonal symmetry

[pearl pond]

@chilly flame Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[midnight haven]

how to factor

[midnight haven]

$x^2 - 23x + 126 = 0$

[white juniper]

quadratic formula perhaps

wait its x there

[jolly parrot]

Book Reader

[midnight haven]

mistype

[white juniper]

ok ok

[midnight haven]

$(x-\frac{23}{2})^2 = \frac{23^2}{4} - 126$

[jolly parrot]

Book Reader

[midnight haven]

$x = +- \sqrt{\frac{23^2}{4} - 126} + \frac{23}{2}$

[limber oasis]

or hope for a nice answer and look for it manually because they tend to do that a lot in exercises

[white juniper]

do you need to complete the square?

[jolly parrot]

Book Reader

[midnight haven]

easier than quadratic formula

[white juniper]

if thats easier for you im not gonna stop you

[feral leaf]

You could always do the AC method of factoring. Find the factor pairs of 126 that sum to -23

[midnight haven]

I'm going to hurt myself

[midnight haven]

never learnt that

[white juniper]

thats true

[limber oasis]

that's what I said
Inconsistent but school

[midnight haven]

okay

i cheated and used desmos because there's no way i'm doing that square root by hand

ty

.close

[pearl pond]

Channel closed

Closed by @light sonnet

Use .reopen if this was a mistake.

[feral leaf]

I just use the discriminant to guess-imate if I can guess the answer or not

[midnight haven]

the factoring was for this btw

horrible fucking question

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wintry mirage]

What does a + b means ?

The ans gv is (1,3) U (3,5) U (5,7)

I have no idea

<@&286206848099549185>

[white juniper]

Name this set C, so if 0 is in A and 1 is in B then 0+1=1 is in C

if 1/2 is in A and 3/2 is in B then 1/2+3/2 = 2 is in C

etc

i think thats what they meant

[wintry mirage]

So just add up the diff numbers from set A and Set B respectively?

[white juniper]

yeah and C would be the set of all possible numbers that can be get that way

[wintry mirage]

What do you get then ?

I list out the possible outcome

[white juniper]

i hope you know that A,B you wrote here are not the same as in original question?

[wintry mirage]

Wdym ?

[white juniper]

in the og question A is set of all real numbers between 0-1 and 2-3

not just 0,1,2,3

so for example 0.1, 0.5, 2.47

etc

[white juniper]

also its not correct even if A,B were correct

[white juniper]

the same goes for B

[pearl pond]

@wintry mirage Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tepid panther]

Is this right?

[pearl pond]

@tepid panther Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[storm panther]

firstly for the seocnd integral

f'(x)=sin(sin(x)) by ftc correct?

how would you get the inverse?

also with the first integral i am on how to compute, since we are intergating with respect to dt we can just take x out correct?

[pearl pond]

@storm panther Has your question been resolved?

[storm panther]

.close

[pearl pond]

Channel closed

Closed by @storm panther

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wintry mirage]

Which terms does it imply for ?

[arctic cave]

What do you mean?

[wintry mirage]

the terms of x^7

[last summit]

My sir @tepid ether can clear this

[arctic cave]

Oh

Alright

[last summit]

Please leave this doubt

My sir will handle it

[wintry mirage]

wtf

[arctic cave]

Errr

What do you mean

[tepid ether]

Hello.

[arctic cave]

Lol

[tepid ether]

Try finding the coefficient of x^7 in each of the terms and adding them all up. I

Do you know the binomial theorem? This is going to be your main tool

[last summit]

✅

[arctic cave]

Yes. To add, you can ignore all the terms before (1+x)^7

[last summit]

!nosols

[pearl pond]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[arctic cave]

Cos their degree is less than 7

[arctic cave]

What do you mean

I'm not giving a solution

Tbh r u just tryna get me outta here

[wintry mirage]

also 10C6 smtg like that ?

[tepid ether]

Sorry sir you should not be choosing 6. Surely the power is equal to 7, right?

[arctic cave]

Yes. If you are confused, we can look at each individual term.

@last summit what r u tryna do

[last summit]

The answer is not 10C6

I was amending your “yes” with a red X to indicate that sir

[arctic cave]

I'm agree with ultimate cjad

Chad

[last summit]

Ah I see. Yes my sir is right

[wintry mirage]

im just giving example dude

[arctic cave]

Alright

[wintry mirage]

Well, the only terms of x^7 i guess only 10C7, bcz i did 10C7 ( 1 + x)^7

which gv me 120x^7

but the ans given 165 ?

[arctic cave]

Ok

We have 4 terms to consider right

(1+x)^7, ^8, ^9, ^10

[wintry mirage]

yup

[arctic cave]

Consider each individual one

(1+x)^7 has coefficient 1 for example

For x^7

[wintry mirage]

10C3 x^3 = 120x^3

[arctic cave]

Ok

Uh sry

[wintry mirage]

i get whatchu mean @arctic cave

i got it 165

[arctic cave]

Oh greattttttt

Anything to clarify?

[wintry mirage]

so far seems good sir

thanks

[wintry mirage]

Another stuff

,rotate

[wintry mirage]

,rotate

[wintry mirage]

,rotate

[wintry mirage]

<@&286206848099549185>

i couldnt find the x^0 terms

[pearl pond]

@wintry mirage Has your question been resolved?

[wintry mirage]

@arctic cave You still here?

[neon sand]

binomial expansion

you can use n choose k to find the coefficients

[pearl pond]

@wintry mirage Has your question been resolved?

Channel closed

Closed by @wintry mirage

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unkempt yacht]

find all positive integer value of $m$ such that $9^{\sqrt{x^2-3x+m}}+2\times3^{\sqrt{x^2-3x+m}-2+x}<3^{2x-3}$ has real solutions

[jolly parrot]

your local hot fungus

[unkempt yacht]

not sure where to start

[midnight haven]

add 3^(2x-4) prob

[unkempt yacht]

what do you mean by this?

[midnight haven]

change lhs to (a+b)²

[cinder flower]

your local hot fungus

[unkempt yacht]

meowdy layla

[cinder flower]

[unkempt yacht]

ah i see what you mean

$(3^{\sqrt{x^2-3x+m}}+3^{x-2})^2<4\times3^{2x-4}$

hm, how would this help us?

[midnight haven]

you should change rhs to 4*3^(2x-4)

[jolly parrot]

your local hot fungus

[midnight haven]

ye now square root

[unkempt yacht]

ohhhhhh

[midnight haven]

u dont need absolute value since theyre all positive

[unkempt yacht]

right

so that should yield us

$3^{\sqrt{x^2-3x+m}}<3^{x-2}$

[midnight haven]

ye

[jolly parrot]

your local hot fungus

[unkempt yacht]

alright thanks for your help, let me calculate the rest

so this should yield

$\sqrt{x^2-3x+m}<x-2$

[jolly parrot]

your local hot fungus

[unkempt yacht]

,,
\begin{cases}
m<-x+4\
m\ge3x-x^2
\end{cases}

[jolly parrot]

your local hot fungus

[unkempt yacht]

so 1, 2, 3, 4

4 roots

alright, thanks!

.close

[pearl pond]

Channel closed

Closed by @unkempt yacht

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[placid sand]

In this question

By integrating

integrating f(x)dx gives me same result

Is there any connection?

[pearl pond]

@placid sand Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[elfin stirrup]

Let $(C([a, b]), \| \cdot \|_{\infty})$ be the Banach space of continuous functions and $K > 0$. We consider the set of functions
\[ M = \{ f \in C^1([a, b]) \, | \, \| f' \|_{\infty} \leq K \} \subset C([a, b]). \]
Show that $M$ is equicontinuous.

[jolly parrot]

tobi

[elfin stirrup]

My Idea was using the Mean Value Theorem to proof this, but I am loosing the supremum while doing this

Im just saying choose eps > 0, and delta = eps/K
because of the mean value theorem, we have ..

[pearl pond]

@elfin stirrup Has your question been resolved?

[elfin stirrup]

<@&286206848099549185>

.close

[pearl pond]

Channel closed

Closed by @elfin stirrup

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[bold wigeon]

Im a bit confused with this, am i just meant to say that when you multiply a complex number, u multiply its modulus and add its argument and since given that C and P satisfy the field axioms, we know that A is closed under multiplication?

[quartz citrus]

pretty much, specifically, if $u,v\in A$ then $|uv|^2 = |u|^2|v|^2 = 1$ and $arg(uv) = arg(u) + arg(v) = p\pi + q\pi = (p + q)\pi$

[jolly parrot]

chebyshev's infinite pee norm

[quartz citrus]

those are the manipulations that justify what you're arguing

[bold wigeon]

Ok thanks alot

.close

[pearl pond]

Channel closed

Closed by @bold wigeon

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pearl pond]

Please don't occupy multiple help channels.

[abstract kraken]

,rotate

[abstract kraken]

What would the bottom restriction be for this question

First part of question is above^

[pearl pond]

@abstract kraken Has your question been resolved?

[pearl pond]

@abstract kraken Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[iron pasture]

Let function f: R -> R has an antiderivative and function g is a polynomial. Prove, that function f×g has an antiderivative.

[pearl pond]

@iron pasture Has your question been resolved?

[iron pasture]

Please, can you help me? I've tried to use per partes rule, but then you have to prove, that antiderivative of f(x) has an antiderivative.

[smoky terrace]

<@&286206848099549185>

[pearl pond]

@iron pasture Has your question been resolved?

[iron pasture]

.close

[pearl pond]

Channel closed

Closed by @iron pasture

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fast nexus]

I need help making a math question based on this NBA post!
Q. Jamal Murray shoots the ball with an initial velocity of 9.25 m/s at an incline of 49.3 degrees. The ball is thrown from a height of 8'11 and reaches a max height of 15.5 inches.

how do I calculate the distance from Murray's hand to the basket?

[fast nexus]

To find time, I did v=u+at, so 0 = 7.03-9.81t, t = 0.71s. Does that work?

and how can I make this question more complex? because im honestly pretty bad at projectiles myself- i'm making it for a friend

[void yew]

I think that is a parabolic path

so linear equations wont work ig??

[fast nexus]

ya

[void yew]

im not so sure

[fast nexus]

oh, wait why?

[void yew]

theres a different formila

for time

in parabola

[fast nexus]

what formula?

[void yew]

t = 2usinTheta/g

[fast nexus]

oh okay

[void yew]

lemme confirm

yeah

thats it

[fast nexus]

so u here is just 9.5ms right? not 9.5cos49.5

*9.25

okay i'm getting 1.43 seconds

is that right?

[void yew]

I havent done it

could u show ur work

[fast nexus]

yaya

(2*9.25 sin 49.5) / 9.81

=1.43399

<@&286206848099549185>

[pearl pond]

@fast nexus Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lone thorn]

how is the integral of e^2x = 1/2e^2x?

[lone thorn]

i get chain rule

but isnt the integal of 2x = x^2

[rose ibex]

well it doesnt work like that

we arent using chain rule, we r integrating

let u=2x and find du/dx to sub in for the dx variable

[lone thorn]

do we have to use substitution for it?

[rose ibex]

well thats the formal way of doing it

[lone thorn]

for e^2x

what if e^2x is part of a bigger equation

[rose ibex]

what is the bigger equation

[lone thorn]

do we have to sub u for the whole equation?

3x^2 -e^2x +1/x

first one is x^3, last is lnx

[rose ibex]

the thing about integrals is that its a linear transformation which means

∫(f(x)+g(x))dx = ∫f(x)dx + ∫g(x)

so u can just separate the terms

[lone thorn]

so we can integrate e^2x with u substituon seperately?

[rose ibex]

yeah

[lone thorn]

ok ill try that now

[rose ibex]

but remember to back-substitute after u get ur integral by letting u=2x again

[lone thorn]

ok i got the right answer

just a quick question with u substition

yk how theres a part where you sub in a function of du for dx?

and then for ex in this case, its (e^u) (du/2)

then 2e^u

but does the du just like dissapear?

[rose ibex]

well yeah 💀

its like ∫3xdx = 3x^2/2

[lone thorn]

I dont get that, how

[rose ibex]

dx is gone

[lone thorn]

is du just telling us to integrate with respect to u? so after u got subbed back out then that automatically removes du?

[rose ibex]

yes

[lone thorn]

ah ok

so du is never actually going to multiply with our function

its only its denominator?

whatever du is over

[wild fable]

u dont do anything with du dx or dy like it just tells you what the function is being integrated with respect to

[lone thorn]

So when multiplying a function by du/whatever, say du/3x, can I think about it like mutliplying that function just with 3x?

[wild fable]

u dont really think of the dx or du multiplying the thing

its not really multiplying

[wild fable]

1/3x

[lone thorn]

howcome then for instance, e^u multiplied by du/2 is 2e^u

if it was mutliplied by 1/2 then shouldnt it be e^u /2?

[wild fable]

um im sorry i dont understand?

what part are u talkingabout

[lone thorn]

ill write it out

[rose ibex]

it is e^u/2

[lone thorn]

1min

[rose ibex]

not 2e^u

[lone thorn]

ohhhhh yeah ur right

I just forgot what the actual answer was mb

[lone thorn]

ok nvm I got it now

[wild fable]

alternatively

u can use this formula

$\int_{ }^{ }f'\left(x\right)e^{f\left(x\right)}=e^{f\left(x\right)}+C$

[jolly parrot]

water beam

[wild fable]

and it doesnt require u sub

[lone thorn]

ooooo

[wild fable]

i think this is quicker and easier, but for more complicated stuff should u sub

[wild fable]

try it with this formula for e^(2x)

whats the derivative of 2x

[lone thorn]

2

[wild fable]

right

but we dont have a 2 at the front right?

[lone thorn]

at the front of e^2x? no we dont

[wild fable]

right

but what we can do

we can slap on a 2

but we cant do this for free

because that would change the function

so we also have to divide by 2

$\frac{1}{2}\int_{ }^{ }2\cdot e^{2x}dx$

[jolly parrot]

water beam

[lone thorn]

does it not cancel out then?

[wild fable]

it can and thats why it works

but look at the formula

we have a 2 at the front right

[lone thorn]

yes

oh wow

maff magic

[wild fable]

so we can use the formula now

so you see how its $\frac{1}{2}\int_{ }^{ }2\cdot e^{2x}dx=\frac{e^{2x}}{2}+C$

[jolly parrot]

water beam

[wild fable]

boom

🪄

[lone thorn]

sorry but half times 2 is 1 so how is it divided by 2 at the end?

[wild fable]

we dont multiply it out

we want to keep the 2 at the front

so we can use the formula

[wild fable]

$\int_{ }^{ }f'\left(x\right)e^{f\left(x\right)}=e^{f\left(x\right)}+C$

[jolly parrot]

water beam

[lone thorn]

ah ok

[wild fable]

remember

we want the derivative at the front for the formula to work

[lone thorn]

and than the second e^fx

is the one multiplied by half?

[wild fable]

which one?

[lone thorn]

which is why its divided by 2?

[lone thorn]

after the equals sign

[wild fable]

its divided by 2 because we had to divide by 2

2/2

=1

[wild fable]

we want the formula to work so there must be a 2 in front of e^2x yes?

2e^(2x)

[lone thorn]

ahhhhhh ok ok

ok tysm for the help and patience 🙏

[wild fable]

u get it now?

[lone thorn]

yeah all good

[wild fable]

nice

[lone thorn]

ty 🙏

.close

[pearl pond]

Channel closed

Closed by @lone thorn

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[midnight haven]

does this look right

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

<@&286206848099549185>

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pulsar spruce]

Hello,

[pulsar spruce]

Is my solution correct?

[calm wing]

yes

[pulsar spruce]

thanks

.close

[pearl pond]

Channel closed

Closed by @pulsar spruce

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[uncut flax]

I need help in a proof of the basis of alternating k-forms

[uncut flax]

The part i dont understand is where it says that the set epsilon_k spans the space of all alternating k-forms

the proof says that after a calculation the unsepecified k-form alfa can be expressed as the sum of this forms but i do not know what calculation to perfprm to reach to that pointç

[pearl pond]

@uncut flax Has your question been resolved?

[pearl pond]

@uncut flax Has your question been resolved?

[fluid axle]

@uncut flax you here still ?

[uncut flax]

yes

[fluid axle]

have you tried anything in the meantime or no ?

[uncut flax]

i have tried but i have not gotten anywhere

as the k-form on the proof alfa is defined for the basis vectors i have tried to separate the vectors in their basis but i have not gotten anyehere

[fluid axle]

you should try only working with bases

if you write to the letter what it means for 2 forms to be equal, you want to check that
$$\alpha(v_1, \cdots, v_k) = \left(\sum \alpha_{i_1, \cdots, i_k}\varepsilon_{i_1, \cdots, i_k}\right)(v_1, \cdots, v_k)$$
for all $(v_1, \cdots, v_k)$ in $V^k$

[jolly parrot]

aPlatypus

[fluid axle]

i.e. for all possible inputs, the forms agree

but you really only need to check equality on a basis of V^k

that's the typical thing that happens in lin alg

if something is true on a basis, then it's true on the whole space

[uncut flax]

okay let me try it

okay i think this is going somewhere

yes because as it is the asociated dual basis, the det as it is defined is 1

i think

but i have to figure out the sum

but is it enought to prove it for the basis vectors?

[fluid axle]

well $\varepsilon_{i_1, \cdots, i_k}(e_{i_1}, \cdots, e_{i_k}) = 1$ sure

[jolly parrot]

aPlatypus

[fluid axle]

there's a lot more other vectors in a basis of V^k though

V^k is n^k-dimensional

you only gave the result of eps_i1...ik for 1 basis vector

[uncut flax]

i dont understand what does he mean when he says to take the sum over the choices of i1,..,ik

[fluid axle]

1 <= i1 < i2 < ... < ik <= n

[uncut flax]

like for all posible combinations?

[fluid axle]

these are the allowed combinations in the sum

[uncut flax]

okay and how would I go about proving it for all posible combinations

[fluid axle]

proving what specifically ?

[uncut flax]

this

[fluid axle]

well what you're interested in is what eps_i1...ik (for any i1, .. ik) outputs for a basis of V^k

n^k possible results you want to be able to summarize

[fluid axle]

the problem here is you can't assume the vectors you input have to match the indices i1, ..., ik of the form eps_i1...ik

[uncut flax]

maybe because of the antysimetry in the sum they go away the ones that do not have that form?

[fluid axle]

not all of them unfortunately

there's still quite a bit of non-zero outputs

maybe you should try a small example

[uncut flax]

no but what i mean is the non-zero outputs still have the antisimetry propierty

and when the sum is performed they go away

[fluid axle]

ok you're going a bit fast though

we still don't even know what an individual eps_i1..ik evaluated on basis of V^k looks like right now

[uncut flax]

i have done it in a pice of paper

[fluid axle]

yeah?

[uncut flax]

yea

its the determinant of a matrix with columns with all 0 and one 1

but in different order

[fluid axle]

the determinant of a permutation matrix then

[uncut flax]

i dont know what that is

okay yes

what im guessing is that for all the clombinations that arent the one that is the identity matrix we can use the alternating propierty to cancel them

but i am not sure

[fluid axle]

no

[uncut flax]

why not=

?

[fluid axle]

the det of a permutation matrix is always -1 or 1 no matter what

[uncut flax]

i know

[fluid axle]

it's not identity matrix or nothing

[uncut flax]

but what i am saying is that when i perfom the sum, as some are + and some are - they go away

if its not this way i dont know how to aproach it

[fluid axle]

that's what should happen yes

[uncut flax]

okay that makes sense

how do i close the chat¿

[fluid axle]

.close

[pearl pond]

Channel closed

Closed by @fluid axle

Use .reopen if this was a mistake.

[uncut flax]

.close

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wanton wave]

I need some help with this one, I know it's already filled in but I just wanna know if I did anything incorrectly because I am unsure with my work and answer. It's about area and perimeter btw!

[wanton wave]

I figured itd be a 30 60 90 triangle bc of the 30°

I thought it qouldve been trig but I think that wouldn't make sense but ya

[neon sand]

,rotate

[pearl pond]

@wanton wave Has your question been resolved?

[wanton wave]

<@&286206848099549185>

[wraith hare]

Firstly, your first answer is 'correct' but you need to round them to nearest tenth. Secondly, your base and height are the wrong way round, the base should be $6\sqrt{3}$ and height should be 6

[jolly parrot]

lgkoo

[wraith hare]

Also, your perimeter is wrong, you cannot just add $12 + 12\sqrt{3} = 24\sqrt{3}$

[jolly parrot]

lgkoo

[wanton wave]

Oh so if it can't be added, should it just be left as a equation?

[pearl pond]

@wanton wave Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rose sentinel]

15 b

[rose sentinel]

Right off the bat I can simplify it to int(u^2cot2xdx)

But after that idk

Because du/dx is -csc2xcot2x

Unless I rephrase it to u du actually

Okay wait

Is it

-csc^2 (2x) / 2

[old marsh]

Yea looks fine I think

[rose sentinel]

Okay thanks

[old marsh]

,w integrate (csc^2 (2x))*cot(2x)

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by northsteve

[old marsh]

Uh oh

[rose sentinel]

Looks like I made a mistake

Oh because

It’s 2x interior so the derivative will bring out the constant 2

So I’d have to devise it out

[old marsh]

Yea

[rose sentinel]

Decide

Decide

Devide

[old marsh]

Divide

[rose sentinel]

Yeah

[old marsh]

Bro lol

[rose sentinel]

I can’t spell 😭

Alright thanks lol

.close

[pearl pond]

Channel closed

Closed by @rose sentinel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[scarlet harbor]

Can someone help me with this? It doesn't have to be complex!

[wet osprey]

How many ways are there to…

[scarlet harbor]

??

the topic is fundamental principle of counting

I'm good with no. 1,i just need help with no. 2

[wet osprey]

Ah

What did you do for part 1?

[scarlet harbor]

A company is organizing a conference with 5 different sessions, each of which can be held in 2 different rooms, and at 3 different time slots. In how many ways can the company schedule the sessions, rooms, and time slots for the conference?

is that correct?

[wet osprey]

Sure

[scarlet harbor]

for no. 2

[wet osprey]

That works

[scarlet harbor]

oh

[scarlet harbor]

can I solve it using 5x2x3

[wet osprey]

Actually that’s not quite right I don’t think

[scarlet harbor]

oh, pls help

[wet osprey]

I think it might depend on the particular wording

It’s usually easier to keep things in terms of either coins, dice or cards

[scarlet harbor]

can u help me with coins?

[wet osprey]

Coins and dice are usually used for non-replacement problems

We want cards here

[scarlet harbor]

I'm rlly not built for create your own situation things

[scarlet harbor]

okay okay, cards

like a deck of cards?

[wet osprey]

Let’s say we have 4 distinct cards, how many ways are there to permute 4 cards?

[scarlet harbor]

for no. 1?

[wet osprey]

Yeah

[scarlet harbor]

so We have 4 cards 3 of it are spades, 2 of it are king, and 1 joker

?

[wet osprey]

Nah nah just think say Ace of spades, hearts, clubs, diamonds

4 distinct cards

[scarlet harbor]

okay

There are 4 cards, they afe ace of spades, hearts, clubs, and diamond

[wet osprey]

This is the question

[scarlet harbor]

ah

[scarlet harbor]

4 ways? Slr my mom asked me to do something

[wet osprey]

ABCD, ABDC, ACBD, ACDB, ADBC, …

There’s more than 4 ways to arrange 4 distinct objects

[scarlet harbor]

I don't get it

[wet osprey]

Do you know what it means to arrange 4 objects?

Or to permute 4 objects?

[scarlet harbor]

Yeah but they want the situation to be 4x3x2x1

[wet osprey]

So the way I think about this is I have 4 boxes or slots

4 different things can go into the first slot